Difference in radius, same power and intensity?

[SPcle]

Homework Statement

How much acoustic power propagates through a spherical surface (sound source in centre) with radius equal to 1.0m? with radius equal to 5.0m?

I = 10^-2 W/m^2
r = 1.0m or 5.0m
f = 50kHz
t = 2.0*10^-3s
IL = 100dB

Homework Equations

I = P/4∏r^2

The Attempt at a Solution

i figured out that when r = 1.0, power must be 1.3*10^-1W. However, when I work out the intensity when r = 5.0, i get:

10^-2 = P/4*∏*25
(10^-2)(4*∏*25) = P
3.1W = P

However, the answer states that the power for both spheres is 0.12W... What concept am I not understanding?

 

[ehild]

It is the same sound source which produces I = 10^-2 W/m^2 at unit distance, so its power is 0.13 W. The same power propagates through any concentric spherical surface, with less and less intensity.

ehild

 

[SPcle]

ooh, i see. so basically the power stays the same because it's the same sound source (a bat, in this case), but the intensity becomes a lot less in distance. i understand now, thanks!

 

[ehild]

ooh, i see. so basically the power stays the same because it's the same sound source (a bat, in this case), but the intensity becomes a lot less in distance. i understand now, thanks!

You understood it quick You are welcome.

ehild

 

[rwisz]

The concept that you may be missing is that power and intensity are not solely dependent on the radius of the spherical surface. They are also affected by the frequency and time parameters provided in the problem. In order to accurately compare the power and intensity at each radius, you would need to use the equation I = P/4∏r^2 and solve for P using the given values for I, r, f, and t. This will result in the same power of 0.12W for both radii of 1.0m and 5.0m.